Spring rate
The number of pounds required to compress the spring 1 inch.
Stiffer springs require more weight to compress than soft springs.

You could also view this is the pounds of force that the spring pushes with after it's been compressed one inch.
It's the same thing.


Motion Ratio
The distance that the spring moves (compresses or expands) is not necessarily the same amount that the wheel moves.
This picture of a coil spring shows that the distance the spring moves (ds) is not the same as the distance that the wheel moves (dw).